One of the tweets targeted President Obama and another alleged that the restaurant would close all of its restaurants at the end of 2015 because the company's food supply had been poisoned by someone with the Twitter account of @TheCeltic666.

That account and another, @TUGFeds, appeared to be suspended by Twitter by Sunday morning. After about three hours or so, what looked to be an apology tweet from Chipotle appeared.

"Our Twitter account was hijacked overnight for about two hours during which a series of offensive tweets was posted to the account," the company's communications director Chris Arnold. "We apologise for the nature of the posts that were made during that time, and we are now conducting an investigation to try to determine what happened and who might have been involved."

Some reports suggested that the company's website suffered some attacks, too, and that traffic had been temporarily hijacked to another Web page.

The @ChipotleTweets account has 630,000 followers. Two years ago, the company faked a hijacking of its Twitter account as part of a 20th-anniversary campaign.